Subgroups — D₃×C₁₉⋊C₃×D₃₁ #35234467

Order 21204.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉⋊C₃×D₉₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₃₁×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉⋊C₃×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₉×D₃₁	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₉⋊C₃×D₃₁	—	3	1	no	maximal
6	C₃×C₃₁×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₁₉⋊C₃×D₃₁	—	2	1	no	—
8	C₁₉⋊C₃×D₃₁	—	3	1	no	—
9	C₁₉⋊C₃×D₃₁	D₃	1	1	yes	characteristic, direct product factor
10	C₁₉×D₉₃	C₂×C₃	1	1	yes	characteristic, complemented
11	D₃×C₁₉×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×C₁₉×D₃₁	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×C₃₁×C₁₉⋊C₃	—	3	1	no	—
14	C₂×C₁₉×D₃₁	—	3	1	no	Hall
15	C₃×C₁₉×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₃₁×C₁₉⋊C₃	—	2	1	no	—
17	C₃₁×C₁₉⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	C₂×C₁₉×C₃₁	—	3	1	no	—
19	C₁₉×D₃₁	—	3	1	no	—
20	C₁₉×D₃₁	C₃×D₃	1	1	yes	characteristic, complemented
21	C₃×D₃×D₃₁	—	19	1	no	maximal, Hall
22	C₂×D₃×C₁₉⋊C₃	—	31	1	no	maximal, Hall
23	C₁₉×C₃₁	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
24	C₃×D₉₃	—	19	1	no	—
25	C₃×D₃×C₃₁	—	19	1	no	—
26	C₃²×D₃₁	—	19	1	no	—
27	C₂×C₃×D₃₁	—	57	1	no	—
28	D₃×D₃₁	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
29	C₂×C₃×C₁₉⋊C₃	—	31	1	no	—
30	D₃×C₁₉⋊C₃	—	31	1	no	—
31	D₃×C₁₉⋊C₃	D₃₁	1	1	yes	characteristic, direct product factor
32	C₃²×C₃₁	—	19	1	no	Hall
33	C₂×D₃×C₁₉	—	31	1	no	—
34	C₂²×C₁₉⋊C₃	—	93	1	no	—
35	C₂×C₃×C₃₁	—	57	1	no	—
36	D₉₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
37	C₃×D₃₁	—	19	1	no	—
38	C₃×D₃₁	—	38	1	no	—
39	C₃×D₃₁	—	57	1	no	—
40	C₃×D₃₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
41	D₃×C₃₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
42	C₃×C₁₉⋊C₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
43	C₂×D₃₁	—	3	1	no	Hall
44	C₂×C₃×C₁₉	—	31	1	no	—
45	D₃×C₁₉	—	31	1	no	—
46	D₃×C₁₉	C₃×D₃₁	1	1	yes	characteristic, complemented
47	C₂×C₁₉⋊C₃	—	3	1	no	—
48	C₂×C₁₉⋊C₃	—	31	1	no	—
49	C₂×C₁₉⋊C₃	—	62	1	no	—
50	C₂×C₁₉⋊C₃	—	93	1	no	—
51	C₃×C₃₁	—	19	1	no	—
52	C₃×C₃₁	—	38	1	no	—
53	C₃×C₃₁	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
54	C₂²×C₁₉	—	93	1	no	Hall
55	C₂×C₃₁	—	3	1	no	—
56	D₃₁	—	3	1	no	—
57	D₃₁	D₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
58	C₃×C₁₉	C₂×C₃×D₃₁	1	1	yes	characteristic, complemented
59	C₁₉⋊C₃	—	2	1	no	—
60	C₁₉⋊C₃	D₃×D₃₁	1	1	yes	characteristic, direct product factor
61	C₂×C₁₉	—	3	1	no	—
62	C₂×C₁₉	—	31	1	no	—
63	C₂×C₁₉	—	93	1	no	—
64	C₂×C₃×D₃	—	589	1	no	Hall
65	C₃₁	C₂×D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
66	C₁₉	C₃×D₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃²	—	589	1	no	—
68	C₃×D₃	—	19	1	no	—
69	C₃×D₃	—	589	1	no	—
70	C₂²×C₃	—	1767	1	no	—
71	C₂×D₃	—	31	1	no	—
72	C₃²	—	19	1	no	Sylow
73	C₂×C₃	—	31	1	no	—
74	C₂×C₃	—	57	1	no	—
75	C₂×C₃	—	589	1	no	—
76	C₂×C₃	—	1178	1	no	—
77	C₂×C₃	—	1767	1	no	—
78	D₃	—	31	1	no	—
79	D₃	C₁₉⋊C₃×D₃₁	1	1	yes	characteristic, direct product factor
80	C₂²	—	93	1	no	Sylow
81	C₃	—	19	1	no	—
82	C₃	—	38	1	no	—
83	C₃	C₂×C₁₉⋊C₃×D₃₁	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	31	1	no	—
86	C₂	—	93	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉×C₃₁	C₂²×C₃
LCS	G ▷ C₃×C₁₉×C₃₁
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₉⋊C₃×D₉₃	C₂	semidirect
2. D₃×C₃₁×C₁₉⋊C₃	C₂	semidirect
3. C₃×C₁₉⋊C₃×D₃₁	C₂	semidirect
4. D₃×C₁₉×D₃₁	C₃	semidirect
6. C₃×C₃₁×C₁₉⋊C₃	C₂²	semidirect
9. C₁₉⋊C₃×D₃₁	D₃	direct (N × H)
10. C₁₉×D₉₃	C₂×C₃	semidirect
11. D₃×C₁₉×C₃₁	C₂×C₃	semidirect
12. C₃×C₁₉×D₃₁	C₂×C₃	semidirect
15. C₃×C₁₉×C₃₁	C₂²×C₃	semidirect
17. C₃₁×C₁₉⋊C₃	C₂×D₃	semidirect
20. C₁₉×D₃₁	C₃×D₃	semidirect
23. C₁₉×C₃₁	C₂×C₃×D₃	semidirect
28. D₃×D₃₁	C₁₉⋊C₃	direct (N × H)
31. D₃×C₁₉⋊C₃	D₃₁	direct (N × H)
36. D₉₃	C₂×C₁₉⋊C₃	semidirect
40. C₃×D₃₁	C₂×C₁₉⋊C₃	semidirect
41. D₃×C₃₁	C₂×C₁₉⋊C₃	semidirect
42. C₃×C₁₉⋊C₃	C₂×D₃₁	semidirect
46. D₃×C₁₉	C₃×D₃₁	semidirect
53. C₃×C₃₁	C₂²×C₁₉⋊C₃	semidirect
57. D₃₁	D₃×C₁₉⋊C₃	direct (N × H)
58. C₃×C₁₉	C₂×C₃×D₃₁	semidirect
60. C₁₉⋊C₃	D₃×D₃₁	direct (N × H)
65. C₃₁	C₂×D₃×C₁₉⋊C₃	semidirect
66. C₁₉	C₃×D₃×D₃₁	semidirect
79. D₃	C₁₉⋊C₃×D₃₁	direct (N × H)
83. C₃	C₂×C₁₉⋊C₃×D₃₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉⋊C₃×D₉₃	2
D₃×C₃₁×C₁₉⋊C₃	2
C₃×C₁₉⋊C₃×D₃₁	2
D₃×C₁₉×D₃₁	3
C₂×C₁₉⋊C₃×D₃₁	3
C₃×D₃×D₃₁	19
C₂×D₃×C₁₉⋊C₃	31

Subgroups — D3×C19⋊C3×D31 #35234467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₁₉⋊C₃×D₃₁ #35234467